Description: This theorem, which is
similar to Theorem 6.7 of [Quine] p. 42 and
holds
under both our definition and Quine's, provides us with a weak definition
of the proper substitution of a class for a set. Since our df-sbc3119 does
not result in the same behavior as Quine's for proper classes, if we
wished to avoid conflict with Quine's definition we could start with this
theorem and dfsbcq23121 instead of df-sbc3119. (dfsbcq23121 is needed because
unlike Quine we do not overload the df-sb1656 syntax.) As a consequence of
these theorems, we can derive sbc8g3125, which is a weaker version of
df-sbc3119 that leaves substitution undefined when is a proper class.

However, it is often a nuisance to have to prove the sethood hypothesis of
sbc8g3125, so we will allow direct use of df-sbc3119 after theorem sbc2or3126
below. Proper substiution with a proper class is rarely needed, and when
it is, we can simply use the expansion of Quine's definition.
(Contributed by NM, 14-Apr-1995.)